# A Spectral Method for Assessing and Combining Multiple Data Visualizations

arXiv: https://arxiv.org/abs/2210.13711 · HTML: https://mlsanity.com/paper/2210.13711/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 60 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [An Analysis of the t-SNE Algorithm for Data Visualization](https://mlsanity.com/paper/1803.01768/) (2018)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Ranking and combining multiple predictors without labeled data](https://mlsanity.com/paper/1303.3257/) (2013)
- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates](https://mlsanity.com/paper/2002.07624/) (2020)
- [What do Asian Religions Have in Common? An Unsupervised Text Analytics Exploration](https://mlsanity.com/paper/1912.10847/) (2019)

## Built on by (most cited first, 6 of 6)

- [Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration](https://mlsanity.com/paper/2507.22170/) (2025)
- [Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators](https://mlsanity.com/paper/2405.12317/) (2024)
- [Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation](https://mlsanity.com/paper/2406.09876/) (2024)
- [Subject clustering by IF-PCA and several recent methods](https://mlsanity.com/paper/2306.05363/) (2023)
- [Consensus dimension reduction via multi-view learning](https://mlsanity.com/paper/2512.15802/) (2025)
- [Visualization of Extremely Sparse Contingency Table by Taxicab Correspondence Analysis: A Case Study of Textual Data](https://mlsanity.com/paper/2308.03079/) (2023)

## Abstract (arXiv)

Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional reduction and visualization algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it critically important to evaluate their relative performance for a given dataset, and to leverage and combine their individual strengths. In this paper, we propose an efficient spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms. The proposed method provides a quantitative measure -- the visualization eigenscore -- of the relative performance of the visualizations for preserving the structure around each data point. Then it leverages the eigenscores to obtain a consensus visualization, which has much improved { quality over the individual visualizations in capturing the underlying true data structure.} Our approach is flexible and works as a wrapper around any visualizations. We analyze multiple simulated and real-world datasets from diverse applications to demonstrate the effectiveness of the eigenscores for evaluating visualizations and the superiority of the proposed consensus visualization. Furthermore, we establish rigorous theoretical justification of our method based on a general statistical framework, yielding fundamental principles behind the empirical success of consensus visualization along with practical guidance.